Finite Group Databasebeta

← #45687611

Subgroups — #45687611

Order 33344.

152 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#30659754C211yesmaximal, characteristic
2#30659741C211yesmaximal, characteristic, complemented
3#30659738C211yesmaximal, characteristic, complemented
4#30659696C211yesmaximal, characteristic, complemented
5#30659636C211yesmaximal, characteristic, complemented
6#30659624C211yesmaximal, characteristic, complemented
7#104×C521C211yesmaximal, characteristic, complemented
8#22552365—21no—
9#22552364—21no—
10#22552364C2211yescharacteristic
11C2×Dic1042C2211yescharacteristic, complemented
12C2×D2084—21no—
13C2×D2084C2211yescharacteristic
14D4×D521—22no—
15D4×D521—21no—
16Dic2084—21no—
17#22552354—21no—
18#22552353—21no—
19#22552352—21no—
20#22552348C2211yescharacteristic, complemented
21#22552341—22no—
22#41×C521C2211yescharacteristic
23M16×C521C2211yescharacteristic, complemented
24C42×C521C2211yescharacteristic, complemented
25C22×D521—22no—
26C22×D521D412yes—
27Dic1042—21no—
28Dic1042—21no—
29Dic1042D411yescharacteristic
30D2084—22no—
31D2084—21no—
32D2084—21no—
33D2084D411yescharacteristic
34C22⋊D521—22no—
35C22⋊D521—21no—
36C2×Dic521—21no—
37C4×D521—22no—
38C4×D521—21no—
39#16861960—21no—
40Q8×C521D411yescharacteristic
41D4×C521—21no—
42D4×C521D411yescharacteristic
43C2×C4×C521—21no—
44C2×C4×C521—21no—
45C2×C4×C521C2311yescharacteristic
46C8×C521—21no—
47C22×C521—21no—
48C22×C521C2×D411yescharacteristic
49C2×D521—22no—
50C2×D521—21no—
51C2×D521—42no—
52C2×D521—82no—
53C4×C521—21no—
54C4×C521—41no—
55C4×C521C2×D411yescharacteristic
56C4×C521C2×D411yescharacteristic
57Dic521—21no—
58Dic521—41no—
59C2×C521—21no—
60C2×C521—41no—
61C2×C521#12011yescharacteristic
62D521—42no—
63D521—41no—
64C521#45511yescharacteristic, complemented, Sylow
65#455—5211nomaximal, Sylow
66H(5,𝔽2)—5211no—
67#137—5211no—
68#137—5211no—
69#124—5211no—
70#104—5211no—
71#104D52111yescharacteristic, complemented
72#100—5211no—
73#41—5211no—
74#41—10421no—
75#41—10421no—
76#41C2×D52111yescharacteristic
77C2×Q8—5211no—
78C2×D4—5211no—
79C2×D4—10421no—
80C2×D4—10422no—
81C2×D4—10421no—
82Q16—10421no—
83Q16—10421no—
84SD16—10421no—
85SD16—10421no—
86M16—5211no—
87M16C2×D52111yescharacteristic, complemented
88C22⋊C4—10422no—
89C42C2×D52111yescharacteristic, complemented
90C23—5212no—
91C23—10422no—
92Q8—5211no—
93Q8—10421no—
94Q8—10421no—
95Q8D208411yescharacteristic
96D4—21no—
97D4—5211no—
98D4—10422no—
99D4—10422no—
100D4—10421no—
101D4—10421no—
102D4—10421no—
103D4D208411yescharacteristic
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—10422no—
107C2×C4—10421no—
108C2×C4—10421no—
109C2×C4C22×D52111yescharacteristic
110C8—21no—
111C8—10421no—
112C22—21no—
113C22—10421no—
114C22—10422no—
115C22—20842no—
116C22—41682no—
117C22D4×D52111yescharacteristic
118C4—21no—
119C4—41no—
120C4—10421no—
121C4—20841no—
122C4D4×D52111yescharacteristic
123C4C2×D208411yescharacteristic
124C2—21no—
125C2—41no—
126C2—20842no—
127C2—20841no—
128C2#3065967811yescharacteristic
subgroupG/H
centerC2#30659678
commutator, cosocleC2×C4×C521C23
FrattiniC2×C4C22×D521
Fitting#104×C521C2
socleC2×C521#120
prime radical#30659754C2
hypercenter#104D521
hypocenterC521#455
LCSG ▷ C2×C4×C521 ▷ C2×C521 ▷ C521
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #30659741C2semidirect
3. #30659738C2semidirect
4. #30659696C2semidirect
5. #30659636C2semidirect
6. #30659624C2semidirect
7. #104×C521C2semidirect
11. C2×Dic1042C22semidirect
20. #22552348C22semidirect
23. M16×C521C22semidirect
24. C42×C521C22semidirect
64. C521#455semidirect
71. #104D521semidirect
87. M16C2×D521semidirect
89. C42C2×D521semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#306597542
#306597412
#306597382
#306596962
#306596362
#306596242
#104×C5212
#455521